## Why is the derivative of $\bf (a^Tx)(b^Tx)=ab^T+ba^T$ and not $2ab^T$?

$$\bf a^Tx$$ is a scalar value. So $$\bf a^Tx=x^Ta$$ so $$\bf (a^Tx)(b^Tx)=x^Tab^Tx$$ which is in quadratic form. So differentiating this gets $$2\bf ab^T$$

However, the book says it is $$ab^T+ba^T$$